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Percolation in the Boolean model with convex grains in high dimension

Jean-Baptiste Gouéré

Abstract

We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K ⊂ R d with non empty interior. In a first setting, the Boolean model is a reunion of translates of K. In a second setting, the Boolean model is a reunion of translates of K or ρK for a further parameter ρ ∈ (1, 2). We give the asymptotic behavior of the percolation probability and of the percolation threshold in the two settings.
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hal-03044355 , version 1 (07-12-2020)

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Jean-Baptiste Gouéré, Florestan Labéy. Percolation in the Boolean model with convex grains in high dimension. 2020. ⟨hal-03044355⟩
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